Integrated circuits (ICs) comprise many transistors and the electrical interconnections between them. ICs and chips have become increasingly complex, with the speed and capacity of chips doubling about every eighteen months. This increase has resulted from advances in design software, fabrication technology, semiconductor materials, and chip design. As feature sizes decrease, the non-ideal nature of the wires between transistors (interconnects) becomes more important. Circuit performance is more affected by the resistance, capacitance, and inductance of these interconnects. In the current generation of technology, and for the near future, signal wavelengths are much larger than the size of a chip. Thus, interconnects can be modeled as RC networks (inductance is typically excluded).
Conventionally, interconnects have been modeled using circuit analysis tools such as SPICE. This involves approximating a distributed system as a lumped system. A distributed system is one where resistance and capacitance are not localized in particular places, but rather spread throughout the entire system. A lumped system is one where particular components of resistance and capacitance are taken to be an accurate representation of all the resistance and capacitance in the system, with the assumption that there is no other resistance or capacitance (for example, over the line between two resistors). Once the lumped element model has been assembled, the circuit impedance (Z) can be found as a function of frequency.
FIG. 1 illustrates a conventional uniform system 2 with conductors 4. System 2 is a distributed system because conductors 4 have different amounts of resistance and capacitance in different places. System 2 may be represented by system 6, which is a lumped system. System 6 is a lumped system because resistors 10 represent all the resistance in system 6, while capacitors 12 represent all the capacitance in system 6.
By making cuts in conductor 4, segments 8 are formed and represented by resistors 10 and capacitors 12 in system 6. In a straight, uniform system such as system 2, making cuts is no problem. The accuracy of the lumped approximation depends on the operating frequency, and the number of resistors 10 and capacitors 12 (elements) used in the model, the latter being a function of the number of cuts made. As more elements are added to the lumped system, it becomes more accurate. One disadvantage of this is that the more complicated the distributed system is, the more time-intensive and expensive it is to calculate an accurate representation of the interconnect impedance. More cuts are required in order to accurately represent a complicated distributed system.
The placement of the cuts as well as the number of cuts will affect the accuracy of the solution. There is no known algorithm that will optimize cut placement. This makes cutting more of an art than a science, taking more time and effort to accurately represent the distributed system.
Accordingly, what is needed is a more cost-effective or efficient method for calculating frequency-dependent impedance in an IC. The present invention addresses such a need.